Question

If $2\left[\begin{array}{cc}x& 5\\ 7& y-3\end{array}\right]+\left[\begin{array}{cc}3& 4\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}7& 14\\ 15& 14\end{array}\right]$, find the value of $x$ and $y$.

Answer 1

We have

$2\left[\begin{array}{cc}x& 5\\ 7& y-3\end{array}\right]+\left[\begin{array}{cc}3& 4\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}7& 14\\ 15& 14\end{array}\right]\left[\begin{array}{cc}2x& 10\\ 14& 2y-6\end{array}\right]+\left[\begin{array}{cc}3& 4\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}7& 14\\ 15& 14\end{array}\right]\left[\begin{array}{cc}2x+3& 10+4\\ 14+1& 2y-6+2\end{array}\right]=\left[\begin{array}{cc}7& 14\\ 15& 14\end{array}\right]$

$2x+3=7$ and $2y-4=14$

$2x=7-3$ $2y=14+4$

$2x=4$ $2y=18$

$x=2$ $y=9$

Hence, this is the answer.